【作者】 樊瑛； 李梦辉； 张鹏； 吴金闪； 狄增如；

【Author】 Ying Fan, Menghui Li, Peng Zhang, Jinshan Wu, Zengru Di ( Department of Systems Science, School of Management, Beijing Normal University, Beijing 100875, PR. China) ( Department of Physics & Astronomy, University of British Columbia, Vancouver, B.C. Canada, V6T 1Z1)

【机构】 北京师范大学管理学院系统科学系；

【摘要】 复杂网络的分析方法已经广泛应用于各个领域,用来描述系统中个体之间的关系以及系统的集体行为。复杂网络最一般的抽象是无权网络,在无权网络中,邻接矩阵A的矩阵元非 0即1,仅表示顶点之间的边存在或不存在两种情况。但在许多情况下,顶点之间的关系或相互作用强度的差异起着至关重要的作用,所以,近几年关于加权网络的研究工作发展很快。目前对加权网络的研究工作主要集中在网络静态统计性质、网络上的物理模型和网络演化模型等几个方面。连接权重可以更细致的刻画系统性质,调整权重也为优化网络性质及功能提供了新的手段;除了改变网络的拓扑结构以外,对加权网络,在给定的拓扑结构基础上,还可以通过调整权重的分布或边-权对应关系来影响网络性质进而优化网络的功能。初步的研究结果表明,在给定网络拓扑的基础上,权重分布的改变可以对网络上Ising模型的相变、混沌振子的同步以及可激发系统的协同振荡等动力学行为产生明显的影响。因此,加权网络研究的核心问题是:理解网络拓扑、物理过程和权重分布三者之间的匹配关系对网络功能的影响。更多还原

【Abstract】 Link Weights, as strength of the interaction represented by networks, are believed to be an important variable in networks. It gives more information about networks besides its topology properties dominated by links. Recently more and more study in complex networks focus on the weighted networks. The problems involve the definition of weight and other quantities which characterize the weighted networks, the empirical studies of its statistical properties, evolving models, and transportation or other dynamics on weighted networks. The fundamental question for weighted networks should be to understand the correlation among topology, dynamics, and weight distribution and their effects on network properties. To known the role of weight, we can consider the difference of some properties between unweighted and weighted networks. Another important way to study the effects of weight is to consider their difference after we disturb the weight distribution. One important property for investigation is community structures. In binary networks, the community structure is defined as groups of network vertices, within groups there are dense internal links among nodes, but between groups nodes loosely connected to the rest of the network. However, link weight should have some important effects on community structures. The definition of the community must integrate links with link weights. Usually, groups separated with the link weights should be different from the result based only on topological linkage. Given the same topological structure, different assignments of link weights may result in different community structures. Many algorithms for community identification have been proposed recently. They detect communities according to topological structures or dynamical behaviors of networks. Most of them are developed for binary networks. But some of them can be generalized to weighted networks. We have discussed performance of several approaches, say weighted GN algorithm, weighted Potts model and WEO methods. Those three algorithms stand for three different approaches: topological structure based, dynamics based, and modularity based. Based on the measure of similarity between community structures, accuracy and precision of three of those algorithms are investigated. Results show that Potts model based algorithm and Weighted Extremal Optimization (WEO) algorithm work well on both dense or sparse weighted networks while Girvan-Newman(GN) algorithm works well only for relatively sparse networks. Then we use WEO algorithm to investigate the effects of weight on community structures. We investigate the different results of partition for non-weighted, weighted, and inverse weighted networks. It is found that weight do have influence on the formation of communities structure. That means: 1, the weight do have important role to the network structures; 2, the community structure is a suitable global properties to reflect the effect of weight. It has been als更多还原